Pulse-train solutions and excitability in an optoelectronic oscillator

Rosin, David P.; Callan, Kristine; Gauthier, Daniel J.; Schöll, Eckehard

doi:10.1209/0295-5075/96/34001

Cited by 41 publications

(29 citation statements)

References 27 publications

(55 reference statements)

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“…The question has been raised by experiments performed on electro-optic oscillators (EOOs), which are modelled mathematically in terms of second-order DDEs [23,24]. An EOO typically incorporates a nonlinear (intensity) modulator, an optical-fibre delay line, and an optical detector in a closed-loop resonating configuration.…”

Section: Introductionmentioning

confidence: 99%

Slow–fast dynamics of a time-delayed electro-optic oscillator

Weicker

Erneux

D'Huys

et al. 2013

Phil. Trans. R. Soc. A.

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International audienceSquare-wave oscillations exhibiting different plateau lengths have been observed experimentally by investigating an electro-optic oscillator. In a previous study, we analysed the model delay differential equations and determined an asymptotic approximation of the two plateaus. In this paper, we concentrate on the fast transition layers between plateaus and show how they contribute to the total period. We also investigate the bifurcation diagram of all possible stable solutions. We show that the square waves emerge from the first Hopf bifurcation of the basic steady state and that they may coexist with stable low-frequency periodic oscillations for the same value of the control parameter

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Section: Introductionmentioning

confidence: 99%

Slow–fast dynamics of a time-delayed electro-optic oscillator

Weicker

Erneux

D'Huys

et al. 2013

Phil. Trans. R. Soc. A.

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“…This strongly suggests their universal appearance. Our findings also show that current knowledge of these hybrid states is far from being complete: Next to the classical chimera state, which exhibits one coherent, phase-locked and one incoherent region, we find a new class of dynamics that possesses multiple domains of incoherence.We consider a ring of N nonlocally coupled FitzHughNagumo (FHN) oscillators, whose relevance is not limited to neuroscience, but also includes chemical [20] and optoelectronic [21] oscillators and nonlinear electronic circuits [22]:where u k and v k are the activator and inhibitor variables, respectively [23,24], and ε > 0 is a small parameter characterizing a timescale separation, which we fix at ε = 0.05 throughout the paper. Depending upon the…”

mentioning

confidence: 99%

When Nonlocal Coupling between Oscillators Becomes Stronger: Patched Synchrony or Multichimera States

Omelchenko

Omel’chenko²,

Hövel³

et al. 2013

Phys. Rev. Lett.

395

427

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Systems of nonlocally coupled oscillators can exhibit complex spatio-temporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multichimera state. We find that, depending on the coupling strength and range, different multi-chimeras arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models. During recent times the investigation of coupled systems has led to joint research efforts bridging between diverse fields such as nonlinear dynamics, network science, and statistical physics, with a plethora of applications, e.g., in physics, biology, and technology. As the numerical resources have developed at fast pace, analysis and simulations of large networks with more and more sophisticated coupling schemes have come into reach giving rise to an abundance of new dynamical scenarios. Among these a very peculiar type of dynamics was first reported for the well-known model of phase oscillators. Such a network exhibits a hybrid nature combining both coherent and incoherent parts [1][2][3][4], hence the name chimera states. The most surprising aspect of this discovery was that these states exist in a system of identical oscillators coupled in a symmetric ring topology with a symmetric interaction function. Recent works have shown that chimeras are not limited to phase oscillators, but can in fact be found in a large variety of different systems. These include time-discrete and time-continuous chaotic models [5,6] and are not restricted to one spatial dimension. Also two-dimensional configurations allow for chimera states [7,8]. Furthermore, similar scenarios exist for time-delayed coupling [9], and their dynamical properties and symmetries were subject to theoretical studies as well [6,10,11]. It was only in the very recent past that chimeras were realized in experiments on chemical oscillators [12] and electro-optical coupled-map lattices [13]. The nonlocality of the coupling -a crucial ingredient for chimera states -also suggests an interesting connection to material science, see, for instance, magnetic Janus particles that undergo a synchronization-induced structural transition in a rotating magnetic field [14,15]. Nonlo- * corresponding author: schoell@physik.tu-berlin.de cality is of great importance not only for chimera states, but also for other dynamical phenomena such as turbulent intermittency [16]. Hybrid states were also reported in the context of neuroscience under the notion of bump states [17]. They were later confirmed for nonlocally coupled Hodgkin-Huxley models [18] and may account for experimental observation of partial synchrony in neu...

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“…Its fields of application range from neuroscience and biological processes [47,54] to optoelectronic [55] and chemical [56] oscillators and nonlinear electronic circuits [57]. We consider a ring of N nonlocally coupled FHN oscillators in the presence of Gaussian white noise:…”

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confidence: 99%

Coherence-Resonance Chimeras in a Network of Excitable Elements

et al. 2016

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We demonstrate that chimera behavior can be observed in nonlocally coupled networks of excitable systems in the presence of noise. This phenomenon is distinct from classical chimeras, which occur in deterministic oscillatory systems, and it combines temporal features of coherence resonance, i.e., the constructive role of noise, and spatial properties of chimera states, i.e., coexistence of spatially coherent and incoherent domains in a network of identical elements. Coherence-resonance chimeras are associated with alternating switching of the location of coherent and incoherent domains, which might be relevant in neuronal networks. Chimera states are intriguing spatio-temporal patterns made up of spatially separated domains of synchronized (spatially coherent) and desynchronized (spatially incoherent) behavior, arising in networks of identical units. Originally discovered in a network of phase oscillators with a simple symmetric non-local coupling scheme [1,2], this sparked a tremendous activity of theoretical investigations . The first experimental evidence on chimera states was presented only one decade after their theoretical discovery [28][29][30][31][32][33][34][35][36][37][38]. In realworld systems chimera states might play a role, e.g., in power grids [39], in social systems [40], in the unihemispheric sleep of birds and dolphins [41], or in epileptic seizures [42]. In the context of the latter two applications it is especially relevant to explore chimera states in neuronal networks under conditions of excitability. However, while chimera states have previously been reported for neuronal networks in the oscillatory regime, e.g., in the FitzHugh-Nagumo system [17], they have not been detected in the excitable regime even for specially prepared initial conditions [17]. Therefore, the existence of chimera states for excitable elements remains unresolved.One of the challenging issues concerning chimera states is their behavior in the presence of random fluctuations, which are unavoidable in real-world systems. The robustness of chimeras with respect to external noise has been studied only very recently [43]. An even more intriguing question is whether the constructive role of noise in nonlinear systems, manifested for example in the counterintuitive increase of temporal coherence due to noise in coherence resonance [44][45][46][47], can be combined with the chimera behavior in spatially extended systems and networks. Coherence resonance, originally discovered for excitable systems like the FitzHugh-Nagumo model, implies that noise-induced oscillations become more regular for an optimum intermediate value of noise intensity. A question naturally arising in this context is whether noise can * corresponding author: anna.zakharova@tu-berlin.de also have a beneficial effect on chimera states. No evidence for the constructive role of noise for chimeras has been previously provided. Therefore, an important issue we aim to address here is to establish a connection between two intriguing counter-intuitive phenomena wh...

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Pulse-train solutions and excitability in an optoelectronic oscillator

Cited by 41 publications

References 27 publications

Slow–fast dynamics of a time-delayed electro-optic oscillator

Slow–fast dynamics of a time-delayed electro-optic oscillator

When Nonlocal Coupling between Oscillators Becomes Stronger: Patched Synchrony or Multichimera States

Coherence-Resonance Chimeras in a Network of Excitable Elements

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